Conventional microscopes suffer from fundamental diffraction effects that limit the resolution to roughly λ/(2×NA), where λ is the optical wavelength and NA the numerical aperture of the imaging system. The numerical aperture (NA) for microscope objectives is at most 1.3-1.6; thus the spatial resolution for optical imaging is limited to around 200 nm for visible light. Images of single nanoscale emitters can be fit to extract the xy position of the object with nanometer precision. This localization precision σ scales roughly as s/N1/2 for photon-limited shot noise, where s is the standard deviation of the microscope's point spread function (PSF) and N is the number of photons detected. In this way, the location of a point emitter can be determined to a much greater precision than the diffraction-limited resolution of an optical system.
Optical imaging systems take light from a three-dimensional (3D) scene and relay it to another position, where typically a camera, eye, or some other photosensitive element is placed. Conventional imaging systems are designed to create two-dimensional (2D) images of 3D scenes, since nearly all photodetectors are 2D (i.e., flat). Thus, it is difficult to extract 3D information from the 2D images created by conventional imaging systems. The primary reason for this difficulty is that the point spread function (PSF), or the image of a point object emitting light, of a conventional imaging system does not vary appreciably as the object moves along the axial direction (closer or father away). Since the conventional PSF does not change very much as an object moves, the conventional PSF does not contain sufficient information about the axial (z) location of an object.